If the slowest of the three pumps can fill the hot tub with water in 90 minutes, then the fastest of the three pumps can fill the same hot tub with water in less than 90 minutes.
To determine the number of minutes it will take for the fastest of the three pumps to fill the hot tub with water, we can use the following formula:
fastest pump's time = (slowest pump's time) / (ratio of fastest to slowest pump)
The ratio of the fastest to slowest pump is not given, but we can assume that all three pumps are equally efficient, so the ratio is 1:3.
Substituting the given value of the slowest pump's time, we get:
fastest pump's time = (90 minutes) / (1/3) = 270 minutes
Therefore, the fastest of the three pumps can fill the hot tub with water in 270 minutes.